SAN FRANCISCO, Jan 8 (Reuters) - California Governor Jerry Brown, a Democrat fresh off a triumphant election in which voters approved higher taxes, will face a new challenge as he presents his proposed budget this week: fending off demands for more spending from his own emboldened party.

The election also gave Democrats a super majority in the state legislature, while the California economy is on the mend and the projected budget deficit is just ${esc.dollar}2 billion - compared with a ${esc.dollar}25 billion shortfall two years ago.

Many are eager to take the rare opportunity to boost spending on education and healthcare programs that have borne billions of dollars in cutbacks.

The liberal wing of the party is agitating for more new taxes, including amendments to the landmark Proposition 13 initiative that limited property tax increases, to help fund social services and other programs. Voters approved an ${esc.dollar}8 billion tax hike in the fall that included higher income taxes for the wealthy and a temporary sales tax increase.

"The legislature is just a pi?ata full of goodies and a lot groups will want to take a whack at it," said Jack Pitney, professor of government of Claremont McKenna College. "Just about anybody who benefits from state services will want more."

Brown's tax hike showed Democrats around the nation that skeptical voters could be persuaded to raise rates under the right circumstances. Now all eyes are on whether California Democrats can use their control to reform the state without overstepping their mandate.

Brown, despite his national reputation as a liberal, has been advocating a fiscally conservative course. He is expected to resist calls for new taxes and more spending on social programs even as he maintains support for big infrastructure projects such as a new water tunnel and a controversial high-speed rail system.

Brown may also face opposition within his party to possible changes in the California Environmental Quality Act, a law that helped establish California's national leadership in environmental protection. Brown has voiced support for amending the law to make it less burdensome to businesses -- a position fiercely opposed by environmentalists.

"They call him a 'canoe' in politics. He paddles to the left, he paddles to the right," said Democratic Assembly member Tom Ammiano of San Francisco. He told Reuters that Democrats should seize the moment, adding that there could be "some clashes" with Brown.

Ammiano may be one of the first to challenge Brown, with a proposal to amend a Proposition 13 provision that lets commercial property buyers avoid new assessments, keeping their taxes low. That idea has failed in the past in the face of passionate support for the tax cap among voters and business interests - but the Democratic supermajority could shift the dynamics of the debate.

DEAL, NO DEAL?

Brown, 74, who served two terms as governor 30 years ago and was again elected in 2010, has two chances this month to set the agenda. He will unveil his budget proposal on Thursday in Sacramento, followed by a State of the State speech in late January.

The state's economic outlook is far better than it was when Brown took office two years ago: employment gains are outpacing the nation, tax collections have rebounded and Standard & Poor's says the state may be on a path to a higher credit rating.

Still, Brown and Democratic Party moderates are preaching restraint.

"We've just got to be careful, strategic," said State Senator Mark DeSaulnier, who represents suburbs of the San Francisco Bay Area. "It's not like we're rich all of a sudden. The fiscal reality is better, but we're a long way from being out of the woods."

Brown's budget will feature a lean spending plan to help the state's books swing to surpluses in coming years, he predicted.

Under pressure, a Democratic lawmaker from Southern California has already retracted a plan floated after the November election for hiking vehicle registration fees.

Some Democratic moderates, distancing themselves from the liberal policies embraced by their San Francisco counterparts, want to focus on making life better for business.

"Before we do anything on taxes, we really need to have a conversation on jobs," said Assembly member Henry Perea, a moderate Democrat from the agricultural, high-unemployment Central Valley.

His top priority is to overhaul the 43-year-old California Environmental Quality Act. Businesses need clarity so they can plan, and the environmental law creates frivolous lawsuits that do not help the environment, he says.

Internecine disagreements within the Democratic Party could kill both tax hikes and any major changes in environmental laws. But the two sides of the party could be close enough to find some common ground, unlike previous Democrat-Republican talks.

Perea said it was not impossible that tax hikes and environmental law changes could all be tied together, for instance, since conservative Democrats are not afraid to strike a deal.

"Moderate Democrats, we're still Democrats, but we are trying to find some balance," Perea said. "The Republicans, they've tried, they did their best to negotiate, but ultimately could never get themselves to a place to say 'Yes.'"

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